We present new lattice results of the K ->pi l nu semileptonic formfactors obtained from simulations with two flavors of dynamicaltwisted-mass fermions, using pion masses as light as 260 MeV. Our mainresult is f(+)(0)=0.9560(84), which, combined with the latestexperimental data for K-l3 decays, leads to|V-us|=0.2267(5)(exp)(20)(f+)(0). Using the PDG(2008) determinations of|V-ud| and |V-ub| our result implies for the unitarity relation|V-ud|(2)+|V-us|(2)+|V-ub|(2)=1.0004(15). For the O(p(6)) term of thechiral expansion of f(+)(0) we get Delta f equivalent tof(+)(0)-1-f(2)=-0.0214(84)....more